Paper:

# Parallel Learning Model and Topological Measurement for Self-Organizing Maps

## Michiharu Maeda^{*}, Hiromi Miyajima^{**}, and Noritaka Shigei^{**}

^{*}Department of Control and Information Systems Engineering, Kurume National College of Technology, 1-1-1 Komorino, Kurume 830-8555, Japan

^{**}Department of Electrical and Electronic Engineering, Faculty of Engineering, Kagoshima University, 1-21-40 Korimoto, Kagoshima 890-0065, Japan

The parallel learning model we propose for self-organizing maps (SOMs) uses reference vectors for simultaneously given multiple input and introduces a topological measurement of ordering for reference vectors in a multidimensional array. We term the parallel SOM algorithm parallel learning and the criterion of ordering the twist index. Parallel learning simultaneously updates reference vectors corresponding to individual input when multiple input is prepared. The twist index is the criterion for evaluating multidimensional ordering of the topological array for reference vectors. When the parallel degree changes for a SOM, the topology preserving map (TPM) for post-learning is evaluated using the twist index. Although adaptation generally yields different results for single and multiple input given at each step in neural networks, parallel learning in SOMs produces results almost the same as sequential learning. Discussing the formation rate of TPMs and average distortion, we examine the effectiveness of our approach through numerical experiments.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.11, No.3, pp. 327-334, 2007.

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